N. Itagaki Yukawa Institute for Theoretical Physics, Kyoto University

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N. Itagaki Yukawa Institute for Theoretical Physics, Kyoto University

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Exotic cluster structure in light nuclei. N. Itagaki Yukawa Institute for Theoretical Physics, Kyoto University. weakly interacting states of strongly bound subsystems. Excitation energy. decay threshold to clusters. single-particle motion of of protons and neutrons. - PowerPoint PPT Presentation

Transcript of N. Itagaki Yukawa Institute for Theoretical Physics, Kyoto University

N. Itagaki Yukawa Institute for Theoretical Physics, Kyoto University

single-particle motion of of protons and neutrons

weakly interacting states of strongly bound subsystems

decay threshold to clusters

Exc

itatio

n en

ergy

Nuclear structure

3α thresholdEx = 7.4 MeV

0+2

Ex =7.65 MeV

0+

2+

Γγ

Γγ

Γα

Synthesis of 12Cfrom three alpha particles

The necessity of dilute 3alpha-cluster state has been pointed out from astrophysical side, and experimentally confirmed afterwards

“Lifetime” of linear chainas a function of impact parameter

How can we stabilize geometric shapes like linear chain configurations?

• Adding valence neutrons

( π )2

( σ ) 2 πσ

N. Itagaki and S. Okabe, Phys. Rev. C 61 044306 (2000)

10Be

1/2+ 3/2- S. Okabe and Y. Abe Prog. Theor. Phys. (1979)

N. Itagaki, S. Okabe, K. Ikeda, and I. TanihataPRC64 (2001), 014301

Linear-chain structure of three clusters in 16C and 20C

J.A. Maruhn, N. Loebl, N. Itagaki, and M. Kimura, Nucl. Phys. A 833 1-17 (2010)

Cluster study with mean-field models

Stability of 3 alpha linear chainwith respect to the bending motion

Dotted -- 16C Geometric shape is stabilizedby adding neutrons

Solid -- 20C

mean-field, shell structure (single-particle motion)

weakly interacting state of clusters

decay threshold to clusters

Exc

itatio

n en

ergycluster structure with geometric shapes

How can we stabilize geometric shapes like linear chain configurations?

• Adding valence neutrons

• Orthogonalizing to other low-lying states

(14C could be possible by Suhara)

• Rotating the system

single-particle motion ofprotons and neutrons

weakly interacting state of clusters

decay threshold to clusters

Exc

itatio

n en

ergycluster structure with geometric shapes

THSR wave function

Gas-like state of three alpha’s around 40Ca?

Hoyle state around the 40Ca core?

Tz. Kokalova et al. Eur. Phys. J A23 (2005)

28Si+24Mg 52Fe

Discussion for the gas-like state of alpha’smoves on to the next step – to heavier regions

Virtual THSR wave function

N.Itagaki, M. Kimura, M. Ito, C. Kurokawa, and W. von Oertzen, Phys. Rev. C 75 037303 (2007)

Gaussian center parameters are randomly generated

by the weight function of

r.m.s. radius of 12C (fm)

Solid, dotted, dashed, dash-dotted σ = 2,3,4,5 fm

Two advantages of this treatment

• Coupling with normal cluster states can be easily calculated

0+ states of 5α system

16O-α model16O-α + 5α gas

N. Itagaki, Tz. Kokalova, M. Ito, M. Kimura, and W. von Oertzen, Phys. Rev. C 77 037301 1-4 (2008).

Two advantages of this treatment

• Coupling with normal cluster states can be easily calculated

• Adding core nucleus is easily done

24Mg = 16O+2alpha’s

7th state, candidate for the resonance stateLarge E0 transition strength

0+ EnergyE0

T. Ichikawa, N. Itagaki, T. Kawabata, Tz. Kokalova, and W von OertzenPhys. Rev. C 83, 061301(R) (2011).

Squared overlap with 16O+2alpha’s (THSR)

28Si =16O+3alpha’s

T. Ichikawa, N. Itagaki, Y. Kanada-En'yo, Tz. Kokalova, and W. von Oertzen, Phys. Rev. C 82 031303(R) (2012)

How about Fermion case?

• Calculation for a 3t state in 9Li, where the coupling effect with the alpha+t+n+n configuration, is performed

• Not gas-like and more compact?

Alpha+t+n+n t+t+t

mean-field, shell structure

Threshold rule:gas like structure clusters

cluster-threshold

Exc

itatio

n en

ergycluster structure with geometric shape

Competition betweenthe cluster and shell structures

α-cluster model

• 4He is strongly bound (B.E. 28.3 MeV)    Close shell configuration of the lowest shell This can be a subunit of the nuclear system

We assume each 4He as (0s)4

spatially localized at some position

Non-central interactions do not contribute

12C 0+ energy convergence

N. Itagaki, S. Aoyama, S. Okabe, and K. Ikeda, PRC70 (2004)

• How we can express the cluster-shell competition in a simple way?

The spin-orbit interaction is the driving force to break the clusters

We introduce a general and simple model to describe this transition

• 12C case

3alpha model Λ = 0

2alpha+quasi cluster Λ = finite

The spin-orbit interaction: (r x p) • s

r Gaussian center parameter Ri

p imaginary part of Ri

For the nucleons in the quasi cluster: Ri Ri + i Λ (e_spin x Ri)

exp[-ν( r – Ri )2]

In the cluster model,4 nucleons share the same Ri value in each alpha cluster

(r x p) • s = (s x r) • p

Slater determinant

spatial part of the single particle wave function

X axis

Z axis

-Y axis

Single particle wave function of nucleons in quasi cluster (spin-up):

Quasi cluster is along xSpin direction is along zMomentum is along y

the cross term can be Taylor expanded as:

for the spin-up nucleon (complex conjugate for spin-down)

the single particle wave function in the quasi cluster becomes

Various configurations of 3α’s with Λ=0

12C

Various configurations of 3α’s with Λ=0

Λ ≠ 0

12C

0+ states of 16C

Λ = 0.8 Λ = 0.8 and 0.0

3α cluster state is importantin the excited states

H. Masui and N.Itagaki, Phys. Rev. C 75 054309 (2007).

We need to introduce an operator and calculate the expectation value

of α breaking

What is the operator related to the α breaking?

one-body spin-orbit operator for the proton part

Various configurations of 3α’s with Λ=0

Λ ≠ 0

12C0.03

0.30

0.28

0.64

one body ls

16C One-body LS

0.440.51

1.45

1.39

18C One-body LS

0.660.64

1.16

1.15

1.09

Breaking all the clusters

Introducing one quasi cluster

Rotating both the spin and spatialparts of the quasi cluster by 120 degree(rotation does not change the j value)

Rotating both the spin and spatialparts of the quasi cluster by 240 degree(rotation does not change the j value)

Energy sufaces

0+ energy

Minimum pointR = 0.9 fm, Λ = 0.2- 89.6 MeV

LS force

Tadahiro Suhara, Naoyuki Itagaki, Jozsef Cseh, and Marek Ploszajczak arXiv nucl-th 1302.5833

One-body spin-orbit operator (p and n)

Comparison with β-γ constraint AMD

986.0)0.2fm,9.0(2

AMDSMSO R

overlap

SMSO AMD

energy - 89.6 [MeV] - 90.1 [MeV]

# of freedom 2 ( R, Λ ) 6A ( 3×2×A )xyz 複素数 粒子数

13C ½- states

Λ=0Λ > 0.1

One-body LS (p)

0.500.010.220.000.55

1.20

Summary• Nuclear structure changes as a function of excitation energy • Geometric configurations are stabilized by adding neutrons

or giving large angular momentum• Studies of gas-like structure of alpha-clusters are extended

to heavier nuclei• Cluster-shell competition and role of non-central

interactions in neutron-rich nuclei can be studied. We can transform Brink’s wave function to jj-coupling shell model by introducing two parameters